WO2002082663A1

WO2002082663A1 - Method and device for coding/decoding a message

Info

Publication number: WO2002082663A1
Application number: PCT/FR2002/001109
Authority: WO
Inventors: Jacques Luder
Original assignee: Thales
Priority date: 2001-04-03
Filing date: 2002-03-29
Publication date: 2002-10-17
Also published as: EP1386403A1; FR2823036A1; FR2823036B1

Abstract

The invention concerns a method and a device for coding/decoding a message. It enables the proper decoding of a message when part of the read message is erroneous. Therefor, a reduced message (RED), whereof the length is less than the original message (MES) is coded with the original message (MES). Said reduced message (RED) enables to reconstruct the possibly illegible parts of the original message (MES). The invention is particularly applicable to coding/decoding of messages on a magnetic tape (BM) track. Said magnetic tapes can be used on hard-cover supports such as parking tickets (TI) or transport tickets or on laminated supports such as identity cards or cards for performing financial transactions.

Description

METHOD AND DEVICE FOR CODING / DECODING A MESSAGE.

The present invention relates to a method and a device for coding / decoding a message. It applies in particular to the coding / decoding of messages on a magnetic tape track. These magnetic tapes can be used on cardboard media such as parking tickets or transport tickets or on plasticized media such as identification cards or cards for carrying out financial transactions.

Magnetic tapes are used to read and write messages, ie sequences of digital data. Data can be written using proprietary or standardized coding. There are many standards and norms issued by organizations such as ANSI (abbreviation of "American National Standards Institute"), ISO (abbreviation of "International Standards Organization"), IATA (abbreviation of "International Air Transportation Association ”), ABA (abbreviation of“ American Bankers Association ”), or THRIFT (banking organization).

Sometimes small areas of a magnetic strip are damaged, making the data written on these areas illegible. When a parking ticket is folded, for example, the data written on the fold is illegible. It also happens that important areas are damaged, making a lot of data unreadable. This happens for example when a parking ticket is stored in a handbag. It can be in contact with a metal clasp or magnetic objects, which can demagnetize an important area of the magnetic track. A known solution to compensate for the loss of data of a message consists in writing this message two or three times on a track of the magnetic tape. During decoding, the first occurrence of the message is read. We then test the integrity of the data read with a longitudinal redundancy code or LRC (Anglo-Saxon abbreviation of "Longitudinal Redundancy Check") for example. If this occurrence of the message is wrong, we can read the second or even the third occurrence. An advantage of this solution is that each occurrence of the message can use standardized coding. A first drawback is that this solution does not allow the message to be decoded correctly if several areas of the magnetic strip are damaged, each making occurrences unreadable.

Another drawback is that this solution doubles or even triples the number of data to be written on a track. However, the number of data that can be written on a track depends on its density on the one hand, and on its length on the other hand. In order to increase the number of data recorded on a track, the maximum length being fixed by the cut of the support, it is necessary to change its density. Increasing the density of a track on a specific medium such as a parking ticket involves modifying all the reading and writing devices already installed. These modifications are accompanied not only by an increase in the price of individual devices, but also by a significant investment when many devices are already installed. An object of the invention is to allow the correct decoding of a message when a part of the message read is erroneous, while limiting the space occupied by the coded message. This object is achieved by the method according to the invention of coding a message (MES) consisting of a sequence of N digital data, which comprises at least the following steps: • a step of reducing the message (MES) to obtain a reduced message (RED) consisting of another sequence of M digital data, where M is strictly less than N, by applying a determined law to the original message such that

• the sequence of data of the original message (MES) being noted where I is a set of N indices, the sequence of data of the reduced message (RED) being noted where Jo is a set of Mo indices, given a surjective application go from I to

Jo associating with each index i of an image j in J ₀ , the data of the original message (MES) are assembled in p-tuples of W _0tj elements, where Woj is an integer, defined by the relation

• the digital data of the original message (MES) and the reduced message (RED) belonging to a set E, given the applications fo _j of the Cartesian product to E associating with each p-tuplet an image in E, the data of the reduced message (RED) are determined by the relationship

• the applications f <j, _j being such that for any p-tuple, it is possible to determine the value of any element of this p-tuple from the values of the other elements on the one hand, and from the value of the reduced message element (RED) on the other hand

• a step of formatting the original message (MES) and the reduced message (RED) to obtain the coded message.

The invention also relates to the decoding method, the recording media, and the coding devices linked to this coding method.

The main advantages of the invention are that it can be compatible with standardized coding methods and that it is simple to implement.

Other characteristics and advantages of the invention will become apparent from the following description given with reference to the accompanying drawings which represent:

• Figure 1 an example of parking ticket with a magnetic strip;

FIG. 2 an example of memory mapping of a message coded according to a known technique;

• Figure 3 an example of analog signal corresponding to a coded message;

• Figure 4, an example of logic signals corresponding to a coded message; • Figure 5 an example of memory mapping of a coded message according to the invention;

FIG. 6 an example of a table used for decoding according to the invention of the coded message in FIG. 4;

• Figure 7 another example of memory mapping of a coded message according to the invention.

We now refer to FIG. 1 in which a TI parking ticket is illustrated. This TI ticket includes a magnetic strip BM on which is written a coded message. This ticket can also include printed symbols such as an LG logo, TXT text. To be read, this ticket TI is inserted in a reader, the front AV of the ticket entering first in reader. The coded message is written on the magnetic strip BM in the form of magnetic codes. These magnetic codes are written in a direction such that the beginning of the coded message is situated at the front AV of the ticket, and the end of the coded message is situated at the rear AR of the ticket. In this way, the coded message can be read at the place.

The coded message consists of a series of bits to which the magnetic codes written on the PI track correspond. This series of bits also corresponds to a series of characters. These characters are of two kinds: data characters on the one hand, and control characters on the other. Data characters can be numeric or alphanumeric characters. In all cases the characters are numeric data.

The original message, that is to say the content of the coded message, is a series of digital data which is represented by the reference MES in the figures. The control characters are inserted automatically when the messages are written by the coders. These control characters make it possible to determine the start and the end of the MES message on the track, and to carry out integrity checks. The format of the coded message corresponds to the correspondence between the series of bits constituting this message, and the series of digital data of the original message MES.

The following standards can be consulted for more information on the magnetic strips used on credit cards, and which can be used for parking tickets too:

Usual codings

Usual runway definitions:

A message is generally coded in a standardized format on one of the tracks on a magnetic tape. There are usually three tracks, numbered 1 to 3, with associated standardized formats:

• Track no. 1, developed by DATA, contains alphanumeric characters for the automation of airline ticketing. It is also used for other transactions in which a reservation database is used.

• Track no. 2, developed by ABA, contains numeric characters for the automation of financial transactions. Today, this track is also used by most systems that require an identification number and a minimum of other control information.

• Track 3, developed by THRIFT, contains information, part of which must be updated (re-recorded) with each transaction. For example, ATMs that operate in offline mode.

Reference is now made to FIG. 2 in which a message coded according to a known technique is represented. This message can be written on a track PI of a magnetic strip, such as the magnetic strip BM of the ticket TI illustrated in FIG. 1. The coded message begins with a margin M1. This margin M1 comprises a series of bits at zero. The length of this margin M1 can be variable. After this margin M1, a start tag (called “start sentinel” in Anglo-Saxon literature) SS indicates the start of the MES message. This starting tag SS is a sequence of determined bits. After this starting tag SS, the coded message comprises the series of N digital data of the original message MES, that is to say the content of the message. After these N data, an end tag (called “end sentinel” in the English literature) ES indicates the end of the message content. This tag is a sequence of determined bits. After this ES tag, a longitudinal redundancy code C1 makes it possible to check the validity of the N data registered. This redundancy code C1 is followed by a second margin M2 of bits at zero until the end of the track. The length of this margin is variable.

Track # 1 (lATA):

We now describe a common example of coding for track 1. Its density is generally 210 BPI. The characters are alphanumeric characters. They occupy 7 bits including 6 data bits Bi, B ₂ , B, B ₄ , B _5f B ₆ and a parity bit P. The parity bit P is determined from the data bits Bi, B ₂ , B ₃ , B, B ₅ , B ₆ . Its value (0 or 1) is such that the total number of bits at 1 in the character is always odd. The first data bit Bi is the least significant bit, the last data bit B ₆ is the most significant bit.

The following table gives the value of the 7 bits according to the character ("Character" column). The first column of the table (“Hex.” Column) is the numeric value of the character (excluding parity bit) in hexadecimal notation.

The abbreviation “hex” will be used after the numbers expressed in hexadecimal notation in the following description. The margin M1 comprises approximately 62 bits at zero. The starting SS tag is the control character "%", ie 05 hex. This control character corresponds to the bit sequence 1010001. The data of the MES message can occupy a maximum of 76 characters. The end tag ES is the control character "? »Ie 1F hex. This control character corresponds to the sequence of bits 1111100. The margin M2 comprises at least 62 bits at zero.

Example (tATA):

The message "TOTO2" is coded as follows

"000 ... 000" the start margin M1 (approximately 62 bits), "101001" the start tag SS, "0010110" the character "T", "1111010" the character "O", "0010110" the character "T", "1111010" the character "O", "0100101" the character "2", "1111100" the end tag ES, "1110110" the longitudinal redundancy code C1, "000 ... 000" the margin M2 end (minimum of 62 bits).

The longitudinal redundancy code is a control character. All characters are valid including "?"", Ie 1F hex. This longitudinal redundancy code C1 is determined by adding by an exclusive OR all the digital data (data characters and control characters) of the coded message from the start tag SS (included) to the end tag ES (included). Then the character parity is determined.

Track # 2 (ABA):

We will now describe a common example of coding for track 2. Its density is generally 75 BPI. Characters are numeric characters. They occupy 5 bits including 4 data bits Bi, B ₂ , B ₃ , B ₄ and a parity bit P. The parity bit P is determined from the data bits B ₁ , B ₂ , B3, B. Its value (0 or 1) is such that the total number of bits at 1 in the character is always odd. The first data bit Bi is the least significant bit, the last data bit B is the most significant bit. The following table gives the value of the 5 bits according to the character ("Character" column). The first column of the table (“Hex.” Column) is the numeric value of the character (excluding parity bit) in hexadecimal notation.

Margin 1 includes approximately 22 bits at zero. The starting tag SS is the control character ";"Ie B hex. This control character corresponds to the sequence of bits 11010. The data of the MES message can occupy a maximum of 37 characters (or 40 characters for the coded message). The end tag ES is the control character "? "Ie F hex. This control character corresponds to the sequence of bits 11111. The margin M2 comprises at least 22 bits at zero.

Track # 3 (THRIFT):

We now describe a common example of coding for track 3. Its density is generally 210 BPI. Characters are numeric characters. They occupy 5 bits in the same way as for track n ° 2.

The margin M1 comprises approximately 62 bits at zero. The M2 margin includes at least 62 bits at zero. The control characters (ES, SS) are the same as for runway 2.

Transcription into magnetic codes and electrical signals:

The magnetic track includes a succession of North (N) and South (S) magnetic poles. Magnetic field lines start from the N pole and go to the S pole. The magnetic tapes include ferromagnetic particles which behave like little magnets. These particles are rigidly retained by a resin. The polarity of these particles is stable. Therefore, these particles behave like permanent magnets. The application of a strong magnetic field of reverse polarity allows the polarity to be changed. The strength of the magnetic field required to produce this effect is called the coercive force. Depending on the particles used, the magnetic tapes are weakly or strongly coercive.

The inscription (recording) of a magnetic tape consists in applying a magnetic field to reveal NS or SN transitions. This application can be carried out with a magnetic writing head comprising a solenoid. This solenoid makes it possible to generate a magnetic field from a voltage. When reading, NS transitions or SN are converted into electrical signals via a read head comprising a solenoid. The passage of this read head on the magnetic strip causes an electrical signal.

There are several ways to write (record) a sequence of 0s and 1s on a magnetic tape. These include the F2F record defined by ISO. "F2F" means frequency / double frequency. We speak of recording with two coherent phases or “Aiken Biphasé” recording. Recording in F2F format allows during playback to generate a clock signal. In other words, the sequence of magnetic codes, transcription of the sequence of bits, allows the reader to generate a clock signal to determine the beginning and the end of the bits read.

This allows the magnetic strip to run in front of the read head without controlling the running speed. Consequently, scanning readers (called “swipe readers” in the English literature), in which the ticket or card is passed manually into a slot, can operate regardless of the speed of passage of the ticket or card in the slot.

Reference is now made to FIG. 3 in which an example of analog signals corresponding to a message written in F2F format is illustrated. The magnetic codes read are converted into an analog electrical signal SIG1. Magnetic field transitions are recorded at a regular period, corresponding to the width of a bit. These transitions allow synchronization. When read, these transitions generate TSYNC signal peaks at a period T1. The 1's are coded by putting an additional transition between two TSYNC synchronization transitions. The 0's are coded without putting an additional transition. Consequently the T2F transitions at the double frequency correspond to ones.

Reference is now made to FIG. 4 in which an example of logic signals generated during the reading of a message in F2F format is illustrated. When reading the message written on the magnetic strip BM, a signal SIG2 indicates the presence of the ticket. A two-level signal SIG3 corresponds to the sequence of bits written on the PI track. A SIG4 sampling signal is generated during reading. It can be generated using a blocking sampler for example. When reading margins (bits with zeros), the period of a T1 bit is determined. After each TSYNC synchronization transition, a monostable flip-flop waits for approximately 75% of (at the period of a T1 bit. If a transition occurs, a bit 1 is read. Otherwise a bit 0 is read. After this duration of 75% of T1, the following transition will be detected, which will serve as a clock signal. The period T2 during which the clock signal is detected has a duration of approximately 25% of T1.

It can happen that a degradation of the support, or a spurious signal alters this signal. Some data read may then be erroneous. The longitudinal redundancy code C1 and the parity bits make it possible to test only the integrity of the content of the MES message. If this content is incorrect, the TI ticket cannot be read.

New coding

Reference is now made to FIG. 5 in which an example of a coded message according to the invention is illustrated. This message can be written on a track PI of a magnetic strip, such as the magnetic strip BM of the ticket TI illustrated in FIG. 1. As in the example illustrated in FIG. 2, the start coded message includes a margin M1 of variable length , a tag SS indicating the beginning of the content of the message MES, the content of the message MES of N digital data, a tag ES indicating the end of the content of the message MES, and a longitudinal redundancy code C1. According to the invention, this longitudinal redundancy code is followed by data determined from the content of the message. This data constitutes a reduced RED message, the length of which is less than that of the original MES message. This reduced message allows the possible unreadable parts of the original MES message to be reconstructed. The reduced RED message can be followed by an ES end tag. This allows in particular the reading of the coded message in both directions. In order to determine the reduced message, the data of the original MES message are assembled in p-tuples. Each element of the RED reduced message is the image by an application of one of these p-upiets. The first element of the reduced message is the image of the first p-tuple, the second element of the reduced message is the image of the second p-tuple, ... In the following description, a mathematical formalism of the sets is used which is recalled in the Engineering Techniques collection, in particular volume AF1 “Mathematical fundamental sciences”, in the article AF33 “Language of sets and structures” by Bernard RANDE from October 1997.

The original message MES comprises N digital data denoted d (i), where i is an index of a set I of N indices. The digital data d (i) can be integers belonging to the set E of integers for example between 0 and 15. We use hexadecimal notations to represent the data d (i).

Using mathematical notations:

MES = with I = {0; 1; 2; 3; ...; N-1}

where with E = {0; 1; 2; 3; ...; 9; A; B; C; D; E; F}

The reduced message RED comprises M ₀ digital data denoted r ₀ (j), where j is an index of a set J ₀ of M ₀ indices. The data r ₀ (j) can be integers belonging to the set E. Using mathematical notations:

RED≈ with J ₀ = {0; 1; 2; 3; ...; M ₀ -1}

or

The data of the original message MES are assembled into pplets noted where j belongs to Jo in the following manner:

where g ₀ is a surjective map from I to J ₀ .

Coding example 1: We take Mo = N / 2. In other words, the reduced RED message is half the size of the original MES message.

The application g ₀ can be the following application:

where od is the modulo function which returns the remainder of the division of i by Mo.

In other words if the message MES is divided into two zones of identical length Z1 and Z2, the zone Z1 corresponding to the first half of the message MES, the zone Z2 corresponding to the second half, each p-tuplet Uo (j) comprises an element of the first zone Z1 and an element of the second zone Z2. In this example, the p-tuples are couples.

More precisely, the first element D1 of the zone Z1 and the first element D4 of the zone Z2 form the first pair u ₀ (0); the second element D2 of zone Z1 and the second element D5 of zone Z2 form the second pair u ₀ (1); ...; the last element D3 of the zone Z1 and the last element D6 of the zone Z2 form the last couple u ₀ (M ₀ -1).

This can be written using the previous mathematical notations as follows: u ₀ (0) = (d (0); d (M ₀ )) u ₀ (1) = (d (1); d (M ₀ +1))

u ₀ (M ₀ -1) = (d (Mo-1); d (N-1))

Each element of the reduced RED message is determined from the preceding p-tuples (of the pairs in this example). The first element D7 of the reduced message RED is the image of the couple (D1; D4) by an application f ₀ , o- The second element D8 of the reduced message RED is the image of the couple (D2; D5) by an application f ₀ , ι ... The last element D9 of the reduced message RED is the image of the couple (D3; D6) by an application

Using mathematical notations we can write: where fo.o, fo, ι, fo, j, are applications.

The applications f ₀ j are such that for any p-tuple u ₀ G), it is possible to determine the value of any element of this p-tuple from the values of the other elements on the one hand, and from the value of the element roG) of the reduced message RED on the other hand.

These applications f ₀ , j can be the following application:

where is a binary operator.

This operator can a logical operator such as an exclusive OR or the negation of an exclusive OR. The values of elements D7 and D8 for example of the reduced message RED are determined by the following relationships:

According to an advantageous embodiment, this operator is a

Exclusive OR, the implementation of which is simple for both coding and decoding. The exclusive OR is represented by the symbol "".

When reading, if the data D1 is illegible for example, it is possible to find it during decoding from D4 on the one hand and from D7 on the other: Similarly if the data D4 is illegible, it is possible to find it from the D1 on the one hand and from D7 on the other:

Thus, it is possible to determine the value of any element of the couple D1, D4 of the couple uo (0) from the values of the other elements on the one hand, and from the value of the element r ₀ (0 ) ie D7 of the RED reduced message on the other hand. It is the same for all the couples UoG) ^{because the} applications f _0j - are all identical in this example. Consequently, the reduced message RED makes it possible to reconstruct any illegible parts of the original MES message. In this example, the reduced message makes it possible to reconstruct up to M unreadable data. In other words, it is possible to read the ticket correctly even if 1/3 of the useful part of the magnetic strip BM is damaged. This applies regardless of where the BM magnetic strip is damaged.

The exclusive OR operator has the other advantage of making it possible not only to reconstruct unreadable parts of the original MES message, but also to carry out integrity checks by zones. In particular, the integrity of the reduced RED message can be checked because its longitudinal redundancy code is the same as that of the original MES message:

Once the RED reduced message has been determined, the original MES message and the RED reduced message are formatted. During a first formatting step, the tag SS is added before the original message MES, the tag ES is added at the end of the original message MES, a longitudinal redundancy code C1 of the original message is determined and added after the ES tag. The reduced RED message is added after the longitudinal redundancy code C1, and a last ES tag is added after. Depending on the length of the PI track, the density of the PI track and the length of the MES message, the length of the margins M1 and M2 is determined. The margin M1 is added before the tag SS, the margin M2 is added after the last tag B3.

During a second formatting step, all of this data (including the margins and the tags) is coded on 5 bits, the first four bits being data bits, the last bit being a parity bit. This parity bit makes it possible to verify the integrity of the character during decoding.

Sometimes the magnetic stripe reader does not correctly read the information on the track. In some cases, the reader returns an uninterrupted series of "1", which could be interpreted by the decoder as a series of characters of code H hex. However, the parity bit of F hex is 1. Consequently, the decoder would not detect a parity error.

According to an advantageous variant, the parity bit of F hex is set to 0 instead of 1. This makes it possible to detect a parity error when the reader returns a long sequence of 1. In fact, it is possible to have at most a sequence of 7 bits to 1 (which corresponds to the sequence of characters of code 3F hex) in integral data.

The following table gives the value of the parity bit according to the character:

The character is represented by its hexadecimal code in the first column of this table on the one hand, and by the value of its four bits in the following columns on the other hand. The first bit B * j is the least significant bit, the last bit B is the most significant bit. The last column of the table is the parity bit P.

According to an equivalent embodiment variant, the inverse of this parity bit is coded, except for F hex. In other words, the value of the parity bit is such that the total number of bits at 1 is always even.

Coding example 2:

In this example, we take N = 40 and M = 15. The go application can be defined by:

Consequently, the MES message data whose rank is between 0 and 19 are assembled in p-tuples of 4 elements, MES message data whose rank is between 20 and 34 are assembled in p-tuples of 3 elements , and the MES message data whose rank is between 35 and 39 are assembled in p-tuples of 1 element (singletons).

In fact, the data of the MES message do not all have the same importance. Thus the data of rank 35 to 39 can be financial data, that is to say critical data. This is why these data are gathered in p-tuples comprising few elements (1 element in this example). In addition, certain areas of the MES message may be more exposed than others. Thus, it is more likely to have a fold at the middle of a ticket only at its start for example. This is why the first data of the MES message (rank between 0 and 19) are assembled in p-tuples of 4 elements, while the following data are assembled in p-tuples of 3 elements only.

The p-tuples u ₀ G) comprising Woj elements, obtained with the previous application g ₀ , are written in the following table:

Each element ro) of the reduced RED message is determined from the preceding UoG) p-tuples as follows:

where fo, o, fo, ι, fo, _j , are applications. These applications f ₀ , j are such that for any p-tupl u ₀ G), it is possible to determine the value of any which element of this p-tuplet from the values of the other elements on the one hand, and the value of the element r ₀ G) of the reduced message RED on the other hand. These applications can be defined as follows:

where is a binary operator. When the p-tuplet includes only one element (for j between 10 and 14), this application is the identity.

The binary operator can an arithmetic operator such as an addition or a subtraction modulo the largest value of E. If this operator is an addition for example, the values of the elements r ₀ G) can be determined by the relations of the following table :

We used the symbol "&" to represent a logical AND. This

Logical AND with the value F hex (ie 15) is equivalent to the modulo operator. In practice, we prefer to use a logical AND whose implementation is simpler and faster. Equivalently, it is possible to add and store the result in a register 4-bit memory. In this way, the deductions beyond the 4 ^{ιemΘ most significant} bit are not memorized, and the logical AND is no longer necessary.

Once the RED reduced message has been determined, the original MES message and the RED reduced message are formatted. The formatting of the coded message can be the same as that of coding example n ° 1 or be another formatting.

Reading and decoding

We will now describe an example of reading and decoding a coded message according to the invention. A first step is to read the coded data. This reading can be carried out by a reading device comprising for example a magnetic reading head making it possible to read the coded message on the magnetic tape. The coded message can be read one way or the other. Advantageously, the coded message is read successively in one direction then in the other.

In this example, the message was coded according to coding example No. 1. The length of the MES message is fixed.

Depending on the direction of reading, the margin M1 or the margin M2 is read first. These margins include bits with zeros. The generated electrical signal resembles a clock signal, which allows synchronization of the reader.

Depending on the direction of reading, the SS tag or the ES tag is read next. Two 15-bit sequences read at the end of the margin (M1 or M2), corresponding to the two read directions, are shown in the following table:

The first line of this table is a numbering of the 15 bits read. The next line contains the sequence of bits read in the first direction

(direction 1) of reading. In this sense, the coded message is read from the right side. The first non-zero bit read is the 11 ^th bit. The first tag read is SS, it's at say the character of code B hex. This code character "B" corresponds to bits 11 to 15 (last five bits): 11010.

The next line contains the sequence of bits read in the second direction (direction 2) of reading. In this sense, the coded message is read backwards. The first non-zero bit read is the I2 ^nd bit. The first tag read is ES, i.e. the code character F hex. The character F hex being read backwards, the first bit read is the parity bit (ie 0 in this example), the next four bits are 1. This character corresponds to bits n ° 11 to 15 : 01111. It is possible to determine the direction of reading from the data read. Indeed, the first bits read are different depending on the direction of reading. This can be useful if no other means makes it possible to determine the direction of introduction of the ticket, in particular for parking tickets whose magnetic strip is in the central position.

The ticket makes a first pass in front of the magnetic reading head of the reader. The data read is memorized. Then the ticket is read the other way. It makes a second pass in front of the read head. The data read in the other direction is memorized. When reading, the integrity of the data is tested. In particular, the parity bits and the longitudinal redundancy code C1 can be used to carry out this integrity test. We can also verify that the data read in both directions are identical. If these read data are not intact, the erroneous data is located. This localization can be done using the parity bits for example.

Example of location of erroneous data n ° 1

We will now describe a first example of reading and locating erroneous data. Reference is made to FIG. 6 in which an example of a table used to store the data read is illustrated. This table TAB can be a table of whole N + Mo, that is to say 1.5 x whole N. These integers can be coded on 16 bits or 32 bits for example to make the addressing of the TAB table faster.

The data memorized during the reading at the place (direction 1) are copied in the table TAB from its beginning DEB1. The tags SS, ES and the longitudinal redundancy code C1 are not copied in this table. The parity bit of the copied data is then checked. The first erroneous parity bit corresponds to non-integral data. We can assume as a precaution that the few data preceding this data are erroneous. For example, the 2 previous data are assumed not to be intact. If no data is detected for a time greater than twice the period of a bit (which happens in the event of a break in the magnetic tape for example), consider that the 2 previous data are not intact.

If the data is entered in F2F format, it is not possible to read the rest of the ticket (loss of clock). Data following non-intact data is unread.

We replace the data assumed not to be intact or unread by a value greater than 15, that is to say greater than the largest possible value read. We then have in the table TAB a range of integral LEC1 data. This data range LEC1 is stored in the start of the table TAB, that is to say from its start DEB1 up to a FINISH limit.

The data memorized during the reverse reading (direction 2) are copied in the table TAB from its end DEB2. Using the parity bits, a second range of integral LEC2 data is similarly determined. Of course, the LEC1 data range is not written. The data range LEC2 is stored in the end of the table TAB, that is to say from its end DEB2 up to a limit FIN2. The elements of the table TAB comprised between the FINI limit and the FIN2 limit correspond to ERR data assumed to be non-intact or unread data.

Of course, if the reading begins in reverse (direction 2) we start by filling the end of the TAB table then we fill the beginning of the TAB table.

Example of location of erroneous data n ° 2:

We will now describe another example of locating erroneous data. It is assumed in this example that there is no loss of clock in the event of an error. We are trying to locate the erroneous data in a data stream. This data flow can be that of the data read during a passage of the magnetic tape in front of the read head. This data stream is processed to detect erroneous data. The result of this processing is a second stream of data. The data of the second stream is marked “integral data” or “non-integral data”. This marking can be performed on a bit (the value 0 for "integral data" and 1 for "non-integral data" for example). This bit can replace the data parity bit of the first data stream.

Each item of data from the first data stream is copied into the second data stream with the marking "integral data" or "non-integral data" depending on the value of the parity bit. This recopy is performed with a delay of two data. In other words, the data of the second data stream is transmitted with a delay of two data.

If a datum is marked "non-integral data" (following an erroneous parity bit), the two preceding data are also marked "non-integral data". Thus, a piece of data can be marked “integral data” at first, then “non-integral data” then. The data following this first datum marked “non-integral data” are also marked “non-integral data” unless the parity bit of the datum to be marked and of the two preceding data is correct. Consequently, a data item is marked "integral data" only if the two preceding data and the following two data have correct parity bits.

We return to the first example of locating erroneous data to describe the rest of the decoding. In the example illustrated in FIG. 6, the data assumed to be non-integral ERR is divided into two parts E1 and E2. The part E1 corresponds to the end of the first half Z1 of the original message MES. Part E2 corresponds to the start of the second half Z2 of the original MES message. The data included in these parts E1 and E2 are missing from the message.

The data corresponding to the part E1 were assembled during coding with a part V2 corresponding to the end of the second half Z2 of the original message MES. The data corresponding to the part E2 was assembled during coding with a part V1 corresponding to the start of the first half Z1 of the original message MES. We use the data of part V1 and of the reduced message RED to determine the data of part E2. Similarly, the data from part V2 and the reduced message RED are used to determine the data from part E1.

Thus, the original MES message is reconstructed in its entirety despite erroneous data. The decoding of the MES message is correct while part of the message read is incorrect. In addition, the coded message occupies only 50% more space compared to a conventional coding which would not allow the message to be reconstructed.

Of course, it is possible to code the message using standardized coding to which the reduced message is added in succession, and a control character (end tag ES for example). This allows you to remain compatible with existing readers. If the length of the MES message is variable, you can adapt the reading simply by using the control characters to measure the length of the MES message. In this case, of course, the data characters and the control characters must have different codes.

encoder

We will now describe an example of a device for recording a message on a recording medium. This device is called an encoder. He understands :

• coding means, intended to implement the coding method described above, making it possible to obtain a coded message from the original message;

• means for writing the coded message, for writing said coded message on the recording medium.

The coding means can be a calculation unit comprising a microprocessor and a random access memory. The writing means depend on the recording medium.

For tickets or cards with magnetic stripes, they may include a magnetic writing head, which is polarized by a head management module. The management module includes an amplifier which amplifies the bias current. These writing means also comprise a stepping motor, which makes it possible to scroll the ticket or the card at constant speed in front of the magnetic writing head.

A quartz makes it possible to synchronize the coding means and the motor, so as to code the ticket or the card with a constant density.

Of course, the invention is not limited to the examples cited. It is possible to implement the invention by coding several reduced messages. Such a coding variant is illustrated in FIG. 7 with two reduced messages RED1 and RED2.

According to this variant, there are 2 steps for reducing the message

MES, to obtain the 2 reduced messages RED1 and RED2. These reduced messages are made up of 2 other sequences of Mi and M ₂ digital data, where Mi and M ₂ are strictly less than N. To this end, 2 determined laws are applied to the original message such as:

• the data sequence of the k ^th reduced message being noted where J _k is a set of M _k indices, given a surjective map g _k from I to J _k associating with each index i of I an image j in J, the data from the original message MES are assembled into p-tuples of W elements, where W _{k, j} is an integer, defined by the relation;

• the digital data of the original message MES and the reduced messages RED1, RED2 belonging to a set E, given the applications f _k of the Cartesian product to E associating with each p-tuple an image in E, the data of the reduced messages RED1, RED2 are determined by the relation _;

• the applications f being such that for any p-tuple, it is possible to determine the value of any element of this p-tuple from the values of the other elements on the one hand, and the value of the element of the reduced message RED1 or RED2 on the other hand During a formatting step, the first reduced message

RED1 can be placed after the original MES message. The second reduced message RED2 is placed after the first reduced message RED1. The first reduced RED1 message can be that of coding example n ° 1. The second reduced RED2 message can be ten times smaller than the original message for example. This second reduced message can be determined in the same way as the first reduced message RED1, the application gi being modified.

In this way the first reduced message RED1 makes it possible to reconstruct up to 50% of the original message MES. If missing data remains, the second reduced message RED2 is then used to reconstruct the sequence. We will manage to reconstruct still up to 10% of the original MES message.

More generally, we can add k reduced messages. The method of coding a message MES consisting of a series of N digital data then comprises the following steps:

• k steps of reduction of the message MES, where k is an integer, to obtain k reduced messages made up of k other sequences of M _k digital data, where M _k is strictly less than N, by applying k laws determined to the original message such as • the sequence of data of the original message MES being noted where I is a set of N indices, the sequence of data of the k ^th reduced message being noted where J _k is a set of M _k indices, given an application surjective g _k from I to J _k associating with each index i of I an image j in J _k , the data of the original message (MES) are assembled in p-tuples of

W _k j elements, where W _k j is an integer, defined by the relation

• the digital data of the original MES message and reduced messages belonging to a set E, given applications f _kιj of the Cartesian product to E associating with each p-tuple an image in E, the data of the reduced messages are determined by the relationship ;

• the applications f _k , j being such that for any p-tuple, it is possible to determine the value of any element of this p-tuple from the values of the other elements on the one hand, and the value of the reduced message element on the other hand

• a step of formatting the original message and reduced messages to obtain the coded message. Of course, it is possible to format the messages in a different way. The invention applies to any type of media or transmission of digital data. Coded messages can be entered in the form of bar codes, for example.

Claims

1. Method for coding a message (MES) consisting of a series of N digital data characterized in that it comprises at least the following steps:

• a message reduction step (MES) to obtain a reduced message (RED) consisting of another series of M ₀ digital data, where

Mo is strictly less than N, by applying a determined law to the original message such as

• the original message data sequence (MES) being noted where I is a set of N indices, the reduced message data sequence (RED) being noted where J ₀ is a set of Mo indices, given an application surjective go from I to

Jo associating with each index i of I an image j in J ₀ , the data of the original message (MES) are assembled in p-tuples of W ₀ , _j elements, where Wo, j is an integer, defined by the relation

• the digital data of the original message (MES) and of the reduced message (RED) belonging to a set E, given applications fo of the Cartesian product to E associating with each p-tuplet an image in E, the data of the message reduced (RED) are determined by the relationship

• the applications f _{0, j} being such that for any p-tuple, it is possible to determine the value of any element of this p-tuple from the values of the other elements on the one hand, and the value of the reduced message element (RED) on the other hand

2. Method for coding a message (MES) consisting of a series of N digital data, characterized in that it comprises at least the following steps:

• k message reduction steps (MES), where k is an integer, to obtain k reduced messages (RED1, RED2) made up of k other sequences of M _k numerical data, where M _k is strictly less than N, by applying k determined laws to the original message such as

• the sequence of data of the original message (MES) being noted where I is a set of N indices, the sequence of data of the k ' ^th reduced message being noted where J _k is a set of M _k indices, given a surjective application g _k from I to J _k associating with each index i of I an image j in J _k , the data of the original message (MES) are assembled in p-tuples of

W _kj elements, where W _k , j is an integer, defined by the relation

• the digital data of the original message (MES) and reduced messages (RED1, RED2) belonging to a set E, given the applications f _k , j of the Cartesian product to E associating with each p-tuplet an image in E , the data of the reduced messages (RED1, RED2) are determined by the relation;

• the applications f _kJ being such that for any p-tuple, it is possible to determine the value of any element of this p-tuple from the values of the other elements on the one hand, and the value of l 'element of the reduced message (RED1, RED2) on the other hand; • a step of formatting the original message (MES) and reduced messages (RED1, RED2) to obtain the coded message.

3. Coding method according to one of the preceding claims, characterized in that for k given, the surjective application is defined by the relation:

where mod is the function modulo which returns the remainder of the division of i by M _k .

4. Coding method according to one of the preceding claims, characterized in that for k given, for all j, the applications f _k j are defined by the relation: where is a binary operator.

5 5. Coding method according to claim 4, characterized in that the binary operator is an arithmetic operator of addition or subtraction type.

6. Coding method according to claim 4, characterized in that o the binary operator is a logical operator of the exclusive OR type.

7. Recording medium (TI) of digital data characterized in that it comprises a recorded coded message resulting from the formatting:

• an original message (MES) consisting of a sequence of N digital data 5;

• and a reduced message (RED) made up of another series of M ₀ digital data, where M ₀ is strictly less than N, the reduced message being able to be deduced from the original message (MES) by determined law such that 0 • the sequence of data of the original message (MES) being noted where I is a set of N indices, the sequence of data of the reduced message (RED) being noted where J ₀ is a set of M indices, given a surjective application g ₀ from I to J ₀ associating with each index i of I an image j in J ₀ , the data 5 of the original message (MES) are assembled in p-tuples of

W ₀ , j elements, where W ₀ , j is an integer, defined by the relation

• the digital data of the original message (MES) and of the reduced message (RED) belonging to a set E, given applications foj of the Cartesian product to E associating with each p-tuplet an image in E, the data of the message reduced (RED) are determined by the relation

• the applications foj being such that for any p-tuplet, it is possible to determine the value of any element of this p-tuple from the values of the other elements on the one hand, and from the value of the element of the reduced message (RED) on the other hand

8. Recording medium (TI) of digital data characterized in that it comprises a recorded coded message resulting from the formatting:

• an original message (MES) consisting of a series of N digital data;

• and k reduced messages (RED1, RED2), where k is an integer, made up of k other sequences of M digital data, where M _k is strictly less than N, the reduced messages can be deduced from the original message

(MES) by k determined laws such as

• the sequence of data of the original message (MES) being noted where I is a set of N indices, the sequence of data of the k ^th reduced message being noted where J is a set of M indices, given a surjective application g _k from I to J associating with each index i of I an image j in J _k , the data of the original message (MES) are assembled in p-tuples of

W _kj elements, where W _{k, j} is an integer, defined by the relation

• the digital data of the original message (MES) and reduced messages (RED1, RED2) belonging to a set E, given the applications f _k of the Cartesian product to E associating with each p-tuple an image in E, the reduced message data (RED1, RED2) are determined by the relation

• the applications f _kj being such that for any p-tuple, it is possible to determine the value of any element of this p-tuple from the values of the other elements on the one hand, and the value of l reduced message element (RED) on the other hand

9. Recording medium according to one of claims 7 to 8, characterized in that for k given, the surjective application is defined by the relation: where mod is the function modulo which returns the remainder of the division of i by M _k .

10. Recording _medium according to one of claims 7 to 9, characterized in that for k given, for all j, the applications f _kιj are defined by the relation:

where is a binary operator.

11. Recording medium according to claim 10, characterized in that the binary operator is an arithmetic operator of the addition or subtraction type.

12. Recording medium according to claim 10, characterized in that the binary operator is a logical operator of the exclusive OR type.

13. Device for recording a message on a recording medium, characterized in that it comprises at least: • coding means, intended to implement the coding method according to any one of claims 1 to 6, making it possible to obtain a coded message from the original message;

14. Method for decoding a coded message, characterized in that the message being coded according to one of claims 1 to 6, the decoding method comprises at least the following steps:

• a step of reading the coded message; • a step for determining erroneous data;

• a step to correct erroneous data.